Periodic spatio-temporal oscillations governed by a globally controlled Ginzburg–Landau equation

• Published in: Physica. D Vol. 240; no. 12; pp. 1036 - 1040
• Main Authors: Kanevsky, Y., Nepomnyashchy, A.A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-06-2011; Elsevier
• Subjects: Asymptotic properties; Complex Ginzburg–Landau equation; Dispersions; Exact sciences and technology; Feedback control; Focusing nonlinearity; Frequency shift; Mathematical analysis; Mathematical models; Nonlinearity; Oscillations; Perturbation theory; Physics; Complex Ginzburg–Landau equation; Focusing nonlinearity; Feedback control; Perturbation theory; Frequency shift; Feedback; Complex Ginzburg-Landau equation; Digital simulation; Nonlinearity; Schroedinger equation; Asymptotic solution; Ginzburg Landau equation; Non linear phenomenon
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2011.03.001

A new type of periodic oscillations in a globally controlled subcritical cubic complex Ginzburg–Landau equation, formerly observed in numerical simulations, is explained and investigated analytically by means of a multiscale perturbation theory. Using an appropriate class of solutions of the nonlinear Schrödinger equation as a starting point, we construct a new class of asymptotic solutions of the cubic complex Ginzburg–Landau equation in the limit of large dispersion and nonlinear frequency shift.
► Adiabatic approximation is applied to nonzero genus solutions of perturbed NSE. ► New class of periodic solutions of globally controlled CGLE is found. ► Stability of obtained solutions is revealed numerically.